Math

Hyperbolas.

Definition

A conic section formed by the set of all points where the absolute difference of distances to two fixed points (foci) is constant. A hyperbola has two separate curved branches that open either horizontally or vertically, with asymptotes guiding their shape.

Examples

Real-world.

  • 1 The path of a spacecraft doing a gravitational slingshot around a planet
  • 2 The shape formed by the shadow of a lampshade on a wall
  • 3 LORAN navigation systems use intersecting hyperbolas to determine position
Key Fact

Standard form: (x−h)²/a² − (y−k)²/b² = 1 (horizontal) or (y−k)²/a² − (x−h)²/b² = 1 (vertical)

Studied in

1 unit use this concept.